Tracking Cation Exchange in Individual Nanowires via Transistor Characterization

Cation exchange is a versatile method for modifying the material composition and properties of nanostructures. However, control of the degree of exchange and material properties is difficult at the single-particle level. Successive cation exchange from CdSe to Ag2Se has been utilized here on the same individual nanowires to monitor the change of electronic properties in field-effect transistor devices. The transistors were fabricated by direct synthesis of CdSe nanowires on prepatterned substrates followed by optical lithography. The devices were then subjected to cation exchange by submerging them in an exchange solution containing silver nitrate. By removal of the devices from solution and probing the electrical transport properties at different times, the change in electronic properties of individual nanowires could be monitored throughout the entire exchange reaction from CdSe to Ag2Se. Transistor characterization revealed that the electrical conductivity can be tuned by up to 8 orders of magnitude and the charge-carrier mobility by 7 orders of magnitude. While analysis of the material composition by energy dispersive X-ray spectroscopy confirmed successful cation exchange from CdSe to Ag2Se, X-ray fluorescence spectroscopy proved that cation exchange also took place below the contacts. The method presented here demonstrates an efficient way to tune the material composition and access the resulting properties nondestructively at the single-particle level. This approach can be readily applied to many other material systems and can be used to study the electrical properties of nanostructures as a function of material composition or to optimize nanostructure-based devices after fabrication.


S1 Crystal structure of nanowires
To determine the morphology and crystal structure of the as grown CdSe nanowires a high-resolution transmission electron microscopy (HRTEM) investigation was performed.Images are shown in figure S1 (a) and (c) along with close-ups of specific areas (white box) in (b) and (d), respectively.[3] Perpendicular to the (002) plane the (100) plane can be observed in figure S1 (d) with a lattice spacing of 3.75 Å nm (3.72 Å, 4 ICSD: 415786).After complete cation exchange to Ag2Se the high crystallinity is preserved, as can be seen in figure S1 (e) and (g), although some new defects have formed.Analysis of the lattice planes in figure S1 (f) and (h) indicate an orthorhombic crystal structure.While the determined spacing of 6.95 Å in figure S1 (f) can be assigned to the (010) plane (7.06 Å, 5 ICSD: 261822) the spacing of 2.57 Å can be attributed to the (121) plane of an orthorhombic lattice (2.59 Å, 5 ICSD: 261822).Nevertheless, the assigned (010) plane (6.95 Å)   could also be interpreted as a (001) plane (7.02 Å, 4 ICSD: 415786) of the hexagonal CdSe host lattice and the (121) plane (2.57Å) as a (102) plane (2.55 Å, 4 ICSD: 415786).
These findings are in accordance with Li et al., 6 where they found that the hexagonal crystal structure of CdSe is maintained after cation exchange to Cu2Se, even though a hexagonal structure of Cu2Se is unusual, and was described as highly unstable.In addition, in a previous report by Dorn et al. 7 the nanowire geometry was also determined to be maintained after cation exchange from CdSe to Ag2Se.They performed a HRTEM investigation after complete cation exchange to Ag2Se to verify the topotaxial nature of the reaction.Indeed, the lattice spacing observed for Ag2Se nanowires fits the previously determined lattice spacing of CdSe.We therefore conclude that the crystal structure after cation exchange likely consists of both a hexagonal CdSe crystal structure and an orthorhombic Ag2Se structure.Previously, we have further confirmed removal of cadmium throughout cation exchange by X-ray diffraction (XRD). 8For this purpose, nanowires were grown as a dense film on a silicon wafer similar to the standard synthesis.To identify reflexes originating from the substrate, it was measured prior to synthesis as well.For the Ag2Se NWs, cation exchange was carried out on a similar sample of CdSe NWs with an increased amount of AgNO3 to compensate for the increased number of NWs and therefore to ensure comparability.The data can be found in the supporting information of the work of Schwarz et al. 8 , here we recap the main findings.
Most reflexes present in the CdSe sample originate from the crystalline silicon wafer.The absence of most reflexes corresponding to CdSe can be explained by the dominant orientation effect as all nanowires lay flat on the substrate, resulting in an underrepresentation of reflexes in growth direction. 9The few reflexes present at 23.8 ° and 42.0 ° were attributed to the wurtzite structure of CdSe.Since the reflex at 42.0 ° can be assigned to the zincblende structure of CdSe as well, together with the absence of other reflexes corresponding to zincblende and the insights from HRTEM, it is concluded that NWs exhibit predominantly wurtzite crystal structure with an admixture of zincblende.Due to an absence of reflexes it was not possible to determine the exact wurtzite-zincblende ratio as shown by Harder et al. 3 Noteworthy is that the reflexes at 27.0 ° (overlapping with wurtzite) and 39.5 ° were assigned to bismuth and most likely result from the recrystallization of the catalyst after melting under synthesis conditions.
After cation exchange to Ag2Se, all reflexes previously assigned to the wafer and bismuth are still present.Furthermore, all reflexes corresponding to wurtzite CdSe are absent, indicating complete cation exchange.Similarly, only few reflexes were observed due to the orientation of the NWs on the substrate.The absence of any peaks indicating the presence of Ag2Se could be a sign of disorder of the cations 10 or stacking faults 11 introduced after cation exchange as observed for various exchange reactions.For Ag2Se, the orthorhombic phase has been observed in HRTEM for nanowires with diameters of 40 nm and larger and is believed to be the most stable phase. 12

S2 Determination of nanowire diameter and channel length
The nanowire diameter and channel length of the fabricated CdSe nanowire field-effect transistors (NWFETs) were determined by atomic force microscopy (AFM).All AFM scans were performed prior to cation exchange to avoid interactions with potential residues from cation exchange.

Figure S2
. AFM scan of a CdSe-NWFET prior to cation exchange.The nanowire diameter is extracted via averaging over several line profiles across the nanowire as marked exemplary in white with the corresponding diameter determined.The channel length is obtained by measuring the distance between the electrodes along the nanowire, as indicated with the double arrow (with an offset to keep the nanowire visible) and the determined length.Note that the thinner second wire is not contacted on both sides and therefore does not contribute to charge transport.
The resolution of an AFM is best in the z-axis (height).Nanowire diameters were determined by averaging over 15 cross-sections of the nanowire in different places, as illustrated in figure S2.For each of these line profiles the background height was fitted and subtracted, and the maximum height was determined.The average of the maxima was calculated and used as nanowire diameter.
For the channel length, the shortest distance between the electrodes along the nanowire was measured (double arrow in figure S2).For a reference sample the nanowire diameter and channel length were additionally determined by scanning electron microcopy (SEM).No significant deviations between SEM and AFM were observed, confirming AFM as a suitable and nondestructive characterization method.

S3 Simulation of the capacitance of nanowire field effect transistors
To determine the charge-carrier mobility  e , the capacitive coupling of the nanowire to the backgate  must be obtained first.In literature, the capacitance is often calculated by using an analytic model for a metallic wire over an infinite metal plate: 13,14 where  r is the dielectric constant of the surrounding medium,  0 is vacuum permittivity,  the channel length, ℎ the distance between nanowire center and gate electrode and  NW is the nanowire radius.This approach assumes that the nanowire is fully surrounded by the dielectric medium (in our case SiO2) instead of a NW lying on top of the dielectric medium (SiO2) with a second dielectric present (Air). 13,14The NW is assumed to be infinite to neglect fringe fields at the electrodes and both gate and nanowire are assumed to be metallic to limit charge accumulation to the surface. 13,14These simplifications lead to significant discrepancies with more detailed models. 13,14gure a significant influence on the capacitance, as shown in figure S3, it was simulated for the dimensions of each device we studied.While most of the effects are considered in this approach, it has to be noted that the nanowire is assumed to be metallic.Since the NWs have a sufficiently high charge-carrier concentration (> 10 18 cm -3 ), this assumption appears reasonable. 13

S4 X-ray fluorescence spectra
In order to verify cation exchange, especially below the contacts, X-ray fluorescence (XRF) was recorded.The XRF maps shown in figure 4 were obtained by extracting the corresponding Kα line intensity of cadmium (23.2 keV) 15 and silver (22.2 keV) 15 of the XRF spectra at each pixel.To illustrate such a XRF spectra, the spectra summed up across the entire scan of figure 4

S5 Thermionic transport model
Non-linear IV curves commonly originate from Schottky barriers at the metal-semiconductor interface. 16Electrons can pass this barrier from the semiconductor into the metal dominantly either by thermionic emission or by tunneling. 16For most semiconductors at room temperature the thermionic emission model is presumed to be the governing transport process. 16,17The current density  then can be described by: 16,17 where  is unit electric charge,  * the effective mass of the charge carriers,  the Boltzmann constant, ℎ is Planck's constant,  the absolute temperature,  B the Schottky-barrier height,  the applied potential and  the ideality factor.The constants in the first part are usually summarized in the Richardson constant  * and by introduction of the saturation current density  S , eq. 1 can be further simplified. 16,17NWFET can be described by two metal-semiconductor interfaces (Schottky diodes) connected back-to-back, therefore the net current of the device is given by the sum of both diodes.
Eq. 1 can then be applied to this metal-semiconductor-metal case, giving: 17 For the sake of simplicity and comprehensiveness we would like to refer to Nouchi 17 who has presented a very detailed derivation of this equation.Both, image-force lowering caused by the applied potential as well as the simultaneous occurrence of forward and reverse current condition need to be taken into account when calculating the Schottky barrier, resulting in the following equation for the barrier height: 17,18  B1 =  B01 +  ( thereby  B1 is the effective Schottky-barrier height and  B01 is the barrier height at zero bias for contact 1 and equally for  B2 ,  B02 for contact 2. 17,18 The effective Schottky-barrier heights  B1 ,  B2 were retrieved by fitting eq. 2 to the measured IV curves together with the adjustments of eq. 3. To convert the current density  to the measured current  the relation  =  •  was used with the assumption that the contact area equals the cross-sectional area of the nanowire . 19Based on the observation that the Ag2Se fraction is mainly responsible for charge-carrier transport the effective electrons mass  * of Ag2Se ( * = 0.32  0 ) 20 was used to calculate the Richardson constant  * .It has to be noted that this approach rests on many assumptions, including that the voltage drops only at the metal-semiconductor interface, which neglects a resistive contribution from the nanowire.Furthermore, the ideality factors  1 ,  2 were used to describe the asymmetry of contacts (in eq. 3) while the ideality factor  (in eq. 2) was set to one which excludes the influence of tunneling current.Wen et al. 21proposed an even more detailed model to consider the influence of thermionic as well as tunneling current, which would go beyond the scope of this analysis.Nevertheless, the applied model is capable of giving an insight into the change of barrier heights with progressing cation exchange.

S6 Introducing silver into contacts
As cation exchange is impeded below the contacts, a potential approach to improve the device response to cation exchange is to partially exchange the metal-semiconductor interface with silver.
The first approach would be to perform a short cation-exchange reaction after lithography prior to metal deposition.However, this is not suitable since the solvents (methanol and toluene) cause a swelling and partial removal of the photoresist.More importantly, the exchange reaction would not be limited to the contact area, given the high mobility of silver ions within the CdSe matrix, resulting in a device with unknown material composition at the beginning of the experiment.
A more suitable approach would be to use silver as contact material.By mild annealing silver could then diffuse into the metal-semiconductor interface leading to a soft doping or exchange of the interface, and ultimately to a lowering of the barrier.We fabricated a device with narrow contacts containing 10 nm Ti as an adhesion layer and a broader 50 nm Ag contact layer (see inset in fig.S6

Figure S1 .
Figure S1.High resolution TEM images of (a-d) CdSe and (e-h) Ag2Se nanowires.(b, d, f, h) Figure S3.(a) COMSOL Multiphysics simulation model used for capacitance estimations.(b) (b) and (c) is shown in figure S4.Besides the signals of interest for cadmium and silver between 22 and 24 keV, signals in the lower energy regime can be found and attributed to various other elements present on the substrate.Prominent peaks around 25.8 and 28.0 keV can be assigned to Compton and Rayleigh scattering, respectively.For better illustration of the Cd and Ag Kα peaks in the inset, the baseline was subtracted from the spectra and smoothed.

Figure S4 .
Figure S4.Raw XRF spectrum summed up of the scan shown in figure 4b and c.The inset shows figure S6 a.

Figure S6 .
Figure S6.(a) SEM image of a device fabricated with Ti/Ag (10/50) nm contacts.The dashed line